The two most prevalent notions of common information (CI) are due to Wyner and to Gács-Körner, and both can be stated as two characteristic points in the lossless Gray-Wyner (GW) region. Although these single letter characterizations of CI can be evaluated for continuous random variables, their operational significance only "makes sense" in the lossless framework. This work generalizes the CI concepts to the lossy GW network in a way that captures their operational significance. The lossy extension of Wyner's CI is the minimum shared rate in GW network at minimum sum rate subject to individual distortion constraints at the two decoders. An example of two Gaussian random variables is solved for the entire distortion regime. Then Gács-Körner's CI is similarly extended to the lossy framework.